Decoding of LDPC codes with binary vector messages and scalable complexity

In this paper, an iterative decoder for LDPC codes, suitable for high-speed processing, is proposed and analyzed. The messages exchanged between the nodes are binary vectors, where the information is conveyed by the number of ones rather than their positions in the vector. Regarding this aspect, the approach exhibits some similarities to stochastic decoding techniques. The check node decoders perform simple bit-wise modulo-2 additions, whereas the variable node decoders perform more complex processing tasks, making the resulting structure attractive for high-speed hardware implementation. By selecting the length of the binary vector messages between one and infinity, the complexity and the performance of the decoder can be scaled between that of the original binary message passing algorithm and that of the sum-product algorithm. Density evolution is developed for the proposed decoding algorithm, and decoding thresholds are determined as functions of the length of the binary vector messages. Simulation results exemplify the performance for finite-length codes.